Mechanistic modelling of tumor kinetics coupled with biomarker dynamics for survival prediction in non-small cell lung cancer patients
Ruben Taieb (1), René Bruno (2), Jin Jin (3), Pascal Chanu (4), Sébastien Benzekry (1)
(1) COMPO (COMPutational pharmacology and clinical Oncology), Inria Sophia Antipolis – Méditerranée and Center for Research on Cancer of Marseille, Inserm U1068, CNRS UMR7258, Institut Paoli-Calmettes, Aix-Marseille University, France; (2) Clinical Pharmacology, Genentech-Roche, Marseille, France ; (3) Clinical Pharmacology, Genentech Inc, South Francisco, USA (4) Clinical Pharmacology, Genentech-Roche, Lyon, France
Objectives:
Simple blood markers derived from routine hematology or biochemistry have been reported to be prognostic factors of overall survival (OS) in cancer patients [1,2]. However, most studies only use baseline (BSL) values. The only longitudinal biomarker that has been extensively used and modeled to date is tumor size kinetics (TK), linked to OS by parametric survival models (TK-OS).
The few studies investigating blood marker kinetics (BK) used simplified empirical or non-coupled models [3,4]. These often fail to capture important correlations and lack a systemic view of the processes at stake [4,5,6]. Non-trivial, complex dynamic BK profiles, either under monotherapy or combination therapy remain to be quantitatively modeled.
We propose here an analysis of the combined kinetics between tumor size and three BKs: albumin, LDH and neutrophils.
Specifically, our aims were to:
(1) Develop a mechanistic model coupling TK with albumin, LDH and neutrophil counts kinetics (denoted TALN-k)
(2) Integrate TALN-k into a nonlinear mixed-effects (NLME) modeling framework to account for inter-individual variability
(3) Assess its goodness-of-fit and benchmark TALN-k against empiric models
(4) Use TALN-k to disentangle complex TK-BK interactions in non-small cell lung cancer patients (NSCLC).
(5) Integrate the selected model-based TALN-k parameters into a ML model for prediction of individual OS.
Methods:
Data
Monotherapy data consisted of the three phase 2 clinical trials POPLAR + FIR + BIRCH (MONO, 862 patients) . Combination therapy data consisted of the phase 3 trial IMpower 150 (COMBO, 1115 patients) with 3 arms composed of combinations of atezolizumab (ATZ) and other agents (bevacizumab and carboplatin + paclitaxel).
TALN-k mechanistic model
TLAN-k is a system of coupled ordinary differential equations (with delay), describing the joint tumor, albumin, LDH and neutrophil counts dynamics under immune-checkpoint inhibition either in monotherapy or in combination with other drugs. The model was derived assuming the following pharmaco-biological hypotheses:
- TK : Tumor cells were divided into two subpopulations with linear growth rate : one resistant , the other sensitive, both with different linear death rates. [8]
- For albumin, LDH and neutrophils, production is regulated and elimination is linear in the absence of tumors.
- Albumin : Albumin production is impaired by tumor-related inflammation, with logistic effect [9] . Inflammation also increases capillary permeability. [6]
- LDH: In addition to physiological production, LDH levels increase when tumor cells die (Warburg effect), [10] but also following neighbouring stroma damage during invasion. [11]
- Neutrophils: Progenitor cells production occurs with linear due to hematopoiesis. They further undergo a three-compartments chain of maturation (variables ) with linear transition rate [4, 12]. Precursor cell production increases with tumour-related inflammation. Chemotherapy effect on neutrophil production was considered to be constant over time. It was thus implicitly modeled in the precursor production parameter .
Population Model
Individual parameters were all assumed to have log-normally distributed random effects, with a diagonal variance-covariance matrix. The error models were combined (constant + proportional) (S), constant (A), proportional (L) andN), which minimized the corrected Bayesian information criterion.
The TALN-k NLME model was fit on the entire tumor, albumin, LDH and neutrophil longitudinal data, on MONO and COMBO separately (total data points: 67,507 COMBO, 44,911 MONO), using the Monolix software and the SAEM algorithm.
Goodness of fit and identifiability were assessed using diagnostic plots, relative standard error (RSE) values and shrinkage of the different estimates.
Definition of the OS prediction problem from on-treatment data
To avoid time-dependent covariate bias for OS prediction, we placed ourselves at cycle 5 day 1 (C5D1, i.e., 3 months after treatment initiation). For each patient, we used only the longitudinal data available before C5D1, to identify their Empirical Bayes estimates (denoted EBEs4 ; 4 as in after 4 cycles). We then discarded the patients who died before C5D1 and computed the shifted OS with C5D1 as baseline for the remaining ones, denoted OS4.
Survival model
The previously defined individual EBEs4 (p = 26 parameters) were adjuncted to baseline covariates (p = 10) to be used as predictors of OS4. Following previous work [13] a random survival forest machine learning (ML) model was chosen and the complete prediction model denoted TALN-kML4. The ML model performances were assesed using 10-fold cross-validation of each dataset. The C-index was considered as the main (discrimination) predictive metric. The 12-months survival area under the ROC curve was also evaluated.
Results:
We found the TALN-k model to fit the data very accurately, with interesting, non-trivial and interpretable individual dynamics and trends, such as early and late peaks of LDH, early drops in albumin, and early drops in neutrophil count.
Despite the relatively large number of parameters (p = 26), practical identifiability was also excellent, with minimal correlation between parameters, low RSEs (all < 27%) and eta-shrinkage (< 9%).
Remarkably, this novel mechanistic model outperformed previous modeling attempts using TK + BK empirical models [13], as evidenced by a substantial decrease in the corrected Bayesian information criterion (difference of 5,883 for COMBO, and 1,819 for MONO).
TLAN-kML4 on COMBO yielded a cross-validation test C-index of 0.67± 0.02 and AUC of 0.78±0.03, versus 0.66 ± 0.04 ; 0.74 ± 0.04 and 0.64 ± 0.04 ; 0.7± 0.06, using TK4 or BSL, respectively).
On MONO, the individual predictions were substantially better than on COMBO. TALN-kml4 yielded a 0.74± 0.02 C-index and 0.83± 0.04 AUC; these dropped to 0.71± 0.03 and 0.78± 0.05 with TK4; and 0.66± 0.02 and 0.72± 0.04 using BSL.
Conclusions:
TALN-k offers interpretability for combined TK-BK dynamics and outperformed previous empirical models. OS prediction was also improved, with better performances for immuno-monotherapy than for immuno-combotherapy.
Such a modeling framework could have 2 main concrete applications:
- To inform indvidual clinical decisions at bedside (personalized healthcare)
- Tointegrateprevious trials and early data to anticipate the outcome of a phase 3 trial, and g. optimize the timing for an interim analysis [7]
- To help assess in Phase 1b, whether a subsequent Phase 3 would be relevant
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